Final answer:
For a spinning record on a turntable at a constant rate, the angular velocity is constant and the angular displacement is constantly changing. The tangential velocity at a point on the record remains constant, thus the arc length traveled over equal time intervals is consistent. Option A is the correct answer.
Step-by-step explanation:
When considering a record spinning on a turntable at a constant rate, the angular velocity is constant. Therefore, option d. The angular velocity is constant is true. Angular velocity is defined as the rate at which an object rotates or revolves relative to another point, which is the rate of change of its angular displacement. In the context of uniform circular motion, since the record is spinning at a constant speed, the angular displacement is constantly changing, affirming option b. The angular displacement is constantly changing.
However, because the speed is consistent, the tangential velocity at a point on the record is also constant, contradicting option c. The tangential velocity of record player is constantly changing, which therefore is false. The tangential velocity varies with radius, but since we're assuming a point moves at a constant distance from the center, its tangential velocity does not change if the angular velocity is constant.
As for option a. The arc length traveled by a point alongside the edge of the spinning record is constantly changing, this is actually false if interpreted over equal time intervals since the speed is constant, resulting in the arc length traveled being the same for equal time intervals. So, the correct statements about the angular velocity of a record spinning at a constant rate are option b and option d.